Field of the Invention
This invention relates to orbit determination of Earth-orbiting satellites and more specifically to the detection and characterization of maneuvers of Earth-orbiting satellites.
Description of the Related Art
Satellites orbiting the Earth are acted upon by many different forces, some of which are hard to accurately characterize and predict. These perturbative forces add significant inaccuracy to predictions of where the satellite will be in the future. For this reason, routine measurements of the satellite's position and velocity are taken, and these measurements are used to update the satellite's estimated orbit. This process of orbit determination is repeated periodically to continue to update the estimate of the satellite's trajectory.
In addition, the perturbative forces acting on satellites cause them to drift from their intended orbits. To restore the satellite to its intended orbit or to move the satellite into a new orbit, operators fire thrusters to maneuver the satellite. Several different kinds of thrusters can be used to maneuver satellites; higher-thrust thrusters such as chemical thrusters are fired for short periods of time (seconds to minutes) to perform a maneuver, and lower-thrust thrusters such as electric/ion thrusters are fired for longer periods of time (tens of minutes to hours) to perform the same size maneuver.
When performing orbit determination on a satellite which maneuvers, accurate modeling of the thrusting force is critical to accurate orbit determination results, and is therefore important to the ability to predict the future position of the satellite.
The process by which measurements of a satellite's position & velocity are used to update the estimated orbit is known as orbit determination (OD). Many types of measurements can be used for orbit determination, for example, range, Doppler, and azimuth and elevation angles can be measured by radars or communication systems; and optical telescopes can measure Right Ascension and Declination angles by comparing the satellite's position against the star background. See Montenbruck, O., and Gill, E. (2001). Satellite Orbits: Models, Methods, and Applications. New York: Springer. pp. 193-288 and Tapley, B. D., Schutz, B. E., and Born, G. H. (2004). Statistical Orbit Determination. San Francisco: Elsevier Academic Press. pp. 93-148 and 159-264.
Standard OD processes use statistical estimation techniques; most often, either a Batch Weighted Least Squares (BWLS) or an Extended Kalman Filter (EKF) is used. Both the BWLS and EKF methods for orbit determination are well known and established. See Montenbruck, O., pp. 257-288 and Tapley, B. pp. 159-263.
Both the BWLS and EKF processes work by computing the predicted position and velocity of the satellite at the time of each measurement, computing the difference between the predicted position/velocity and the measured data—a quantity known as the measurement residual—and using the estimation technique to calculate an updated satellite trajectory which best fits the measurements used. The two major techniques differ primarily in that a BWLS process computes the residuals of a “batch” of measurements and combines all the information to compute an updated orbit, whereas an EKF sequentially processes each measurement and computes an updated orbit at each measurement. FIG. 1 shows an illustration of the residuals 10 for a good orbit determination on a satellite tracked by 3 sensors. A “perfect” orbit determination would fit all the measurements exactly, making the residuals all zero. Due to noise and other errors on the measurements, as well as imperfect modeling of the forces acting on the satellite, residuals are always non-zero. A good orbit determination will reduce the residuals to just noise, or nearly just noise, as shown in the figure.
Both BWLS and EKF-based orbit determination processes also produce statistical estimates of the error in the orbit solution—this data is represented by the covariance. All OD processes produce a covariance matrix as part of the estimation computations, but each OD process may add custom “process noise” factors to the covariance to better represent the true orbit error.
FIGS. 2A-2C illustrate the importance of correctly modeling maneuver effects when performing orbit determination. FIG. 2A shows the residuals 12 from 3 sensors for a good pre-maneuver OD run with small residuals from February 16th-18th, and shows the effects of a maneuver early on February 18th on the measurement residuals. FIG. 2B shows the residuals 14 for an OD run which includes the post-maneuver measurements but does not model the effects of the maneuver—fit quality here is clearly poor. FIG. 2C shows the OD residuals 16 if the maneuver is correctly modeled—measurement data before and after the maneuver fits well.
Maneuver detection and characterization techniques fall into three general types:
a) Once measurement data no longer fits the old orbit, use a simple manual or automated iteration to try to isolate approximately when the maneuver occurred, and then start an entirely new orbit determination using only post-maneuver data.
b) Once measurement data no longer fits the old orbit, add process noise to the orbit determination process to increase the size of the covariance and allow the measurement data to be used.
c) Once measurement data no longer fits the old orbit, assume the maneuver is in the “in-track” direction (the direction of satellite motion), and use the initial post-maneuver measurement data to solve for a change in orbit energy or equivalently, semi-major axis.
These known maneuver detection and characterization techniques are generally incapable of fitting the measurement data before, during and after the maneuver.